13 feet was to avoid most of the effects of refraction, I believe. But in any case the two bridges would afford the simplest method. Still thinking about this. The canal boat forums suggest that the river is silted up, and a canal boat would have difficulty. Might be possible to drive a pole into the river bed. Not sure.

"First. The test proposed at p. 5, to place a spirit-level at the middle station, and take a sight both ways to Welney Bridge and Old Bedford Bridge (not Welche's Dam as you state) the water at the two ends would certainly be shown to be about five feet below the horizontal straight line touching the water at the middle station. The only difficulty would be in getting the level placed high enough to be above the vapours and unequally heated air close to the ground; but I have no doubt, if it were placed on the elevated towing path, its height above the water would be about five feet less than the height of the points on the two bridges cut by the cross-hair, which determines the true level line. https://people.wku.edu/charles.smith/wallace/S179AA.htm

I have belatedly realised that on Google Earth (at least in the current version with imagery dated 1/1/2007) the land near Welney to the south-east of the Old Bedford River is actually flooded. This tends to obscure the fact that there are two waterways running parallel near Welney: the Old Bedford River and the River Delph. (This is clearer if you zoom in on the map I just linked to.) In consequence, there are currently two bridges at Welney, one over the OBR and one over the Delph. As Rory pointed out, the one over the OBR might well be called the Old Bedford Bridge, but it might equally be called the Welney Bridge to distinguish it from other bridges over the OBR. I do not know if there were two bridges in 1870. [Edit: two bridges are shown in the 1886 OS map shown mentioned earlier in this thread.]

It can be difficult to understand what FE believers are thinking. I think I've finally figured out what it is that's bothering them in this case. Part of the confusion is that both sides have been assuming they are thinking of this as a problem with perspective. But the problem, as they conceive it, is not one of perspective; it's parallax.

In the Wallace experiment, the critical factor is the elevation of the observer's telescope above the water surface. The instrument does not need to be leveled, because the distant targets will retain their relative positions to one another no matter how the telescope is tilted - up & down or side to side. As long as the targets are all in the field of view they will retain exactly the same relative position to one another.

If the observer's telescope were on an elevator, and if the elevator moved up or down, there would be a parallax shift, and the relative positions of the targets would change. Same thing if it were mounted on a car and the telescope were moving on the horizontal.

Here's the crux. These FE believers feel that tilting the telescope will cause a parallax shift; and the relative positions of the target will change. I think that's why, all those years ago, Carpenter insisted that the instrument be leveled and have a reticle (cross-hairs). And perhaps he was bothered by the fact that the horizontal line of the reticle was above the targets, I don't know.

In this case it wouldn't matter if one used three targets or more. They would have the same objection: the telescope might be tilted, however microscopically, thus changing the relative positions of the targets, and giving the false impression that they are not positioned in a straight line.

The first step is to clear up this misconception. Perhaps a video showing that this doesn't happen. A video camera on a tripod, demonstrating that there is no parallax shift when the camera is tilted or moved from side to side.

I think that, in this case, these people are simply associating, through life experience, movement with parallax shift. Tilting is a movement, so they feel that tilting the telescope will cause a parallax shift. This misunderstanding disappears if one thinks about the problem analytically (system 2), but they haven't taken this step. I predict that they will resist doing so.

I have belatedly realised that on Google Earth (at least in the current version with imagery dated 1/1/2007) the land near Welney to the south-east of the Old Bedford River is actually flooded. This tends to obscure the fact that there are two waterways running parallel near Welney: the Old Bedford River and the River Delph. (This is clearer if you zoom in on the map I just linked to.) In consequence, there are currently two bridges at Welney, one over the OBR and one over the Delph. As Rory pointed out, the one over the OBR might well be called the Old Bedford Bridge, but it might equally be called the Welney Bridge to distinguish it from other bridges over the OBR. I do not know if there were two bridges in 1870. [Edit: two bridges are shown in the 1886 OS map shown mentioned earlier in this thread.]

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There are indeed two waterways, but Wallace clearly says, in a number of places 'old Bedford river', not Delph river.

The first step is to clear up this misconception. Perhaps a video showing that this doesn't happen. A video camera on a tripod, demonstrating that there is no parallax shift when the camera is tilted or moved from side to side.

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This is entirely correct. Two markers are enough, with the third point being the viewpoint of the viewer. Three would work, however my fundamental principle is to make an experiment no more complicated than necessary to prove the point. Wallace complicated it by adding a level with a cross hair, as well as a telescope, as though a cross hair was needed.

I have already had a similar conversation with an FEer at another forum. He claims that refraction in the telescope will cause the position of the markers to change.

It is crucial for any FE observer to agree in advance what observations would prove or disprove either theory. It seems as though Wallace didn’t do this, given that Hampden and Carpenter were ‘whooping with joy’ when they looked through the lens. Wallace later went through the logic, see the many letters in The Field and other publications at the time, but too late. The scientific method is to construct a model to predict what observations will be. Then run an experiment to see if observation is consistent with the model. If repeated experiments show not, then reject the model.

Yes, the kind of video you suggest might be conclusive. However I only came across this FE thing a few days ago, and my eyes have been opened. One difficulty, as I mentioned above, is any chain of reasoning involving more than two premises.

PS as I mentioned above, the proof essentially relies on the assumption that if X and Y are parallel, i.e. equidistant at every place, and X is straight, then Y is straight.

In this case, let X be the straight line made by three markers, and Y the surface of the water.

We then only have to prove that the three points make a straight line. This we do by having a far point C (Old Bedford Sluice), a mid point B (pole on a barge) and a near point A (observer's eye on Welney Bridge). If B and C line up, i.e. if B is right in front of C, then the three points form a straight line.

One difficulty, as I mentioned above, is any chain of reasoning involving more than two premises.

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Because, while thinking in system 1, every thought is an isolated and immutable association. This is the infamous Filing Cabinet Syndrome. Each thought or belief has its own file folder in the cabinet and only one folder can be open at a time. When a new thought - or "file folder" - is brought out, the previous one is put away. Thus the cabinet can hold mutually exclusive thoughts, nestled in individual folders.

Or in this case, the thoughts cannot be put into a chain of reasoning.

A person who uses this mode of thought, when angered, puts away the folder in discussion, and pulls out one he thinks is relevant. E.g. - where's the curve? Or in the debate at hand, he will refuse to put away the folder marked "the targets will change position." Emotion keeps him in system 1.

Everyone does this to some extent. It's just that some people are more prone than others.

I have already had a similar conversation with an FEer at another forum. He claims that refraction in the telescope will cause the position of the markers to change.

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This is a rationalization defending the feeling that tilting causes a parallax shift - or in a larger sense, FE itself. There is nothing in the science of optics that would suggest or support this, and I'm certain that this idea did not come from any knowledge of optics. It was pulled out of a hat.

Mick, could you explain the 40 PVC tubing bit please? I am thinking, a tripod structure that goes into the water with weights to hold it down, then a straight bit to give the required height above the water. Is it possible to construct such a thing? We would have to get permission from the Environmental Agency, probably. Given we don't know the depth of the water, there would have to be a method of adjusting the height.

My handyman attributes about 3 out of 10.

We could ask someone in the canal boat community to help out, but it seems the water too silted up to get to that stretch.

March 6th 2020 would be the date, but could have a dry run, probably rather a wet one, well before then.

This illustrate the issue of getting the right weather and time of day:

However it might also illustrate the, to a degree, the markers are already in place. We are looking UP at the bottom of the railway bridge, which appears to be twice as as high as distant objects.
How high is the bottom of the railway bridge above the waterline? Suppose we were to find out that height, and then set the camera at the same height, then a distant target also at the same height.

I suspect in this video the camera is not far off the correct height already.

And what are we looking at here?

Probably just trees. but at the other end we have the pump-house bridge, where some "experiments" have been done from. This is where the "calico sheet" target would be.
An alternative to a target might simply be to drive a bright colored car or truck back and forth over the bridge. The motion would greatly aid with visibility, and the vehicle is of known height.

And thinking about all of this. A first step would be to obtain high quality measurements of the the respective heights of the tree bridges above the waterline. This should be relatively easy. But I'd suggest making a high visibility marked measuring pole (white PVC, black tape every 3 inches, double width band every 1 foot ) for video verification of the measurements.

Schedule 40 is just the type of PVC tubing used for household pressure water lines in garden irrigation. I've got lots of it at my house. It's stiff, you can cut it to size, and it has couplings that let you just push pieces together to make longer pieces, or structures like bases. It comes in different diameters, but 1" diameter should work

This is a rationalization defending the feeling that tilting causes a parallax shift - and in a larger sense, FE itself. There is nothing in the science of optics that would suggest or support this, and I'm certain that this idea did not come from any knowledge of optics. It was pulled out of a hat.

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He has just come back, and evaded the 'different angle' objection. He now claims that even if the observation point is shifted up or downwards, right or left, even by a fraction of an inch, the observation will change. He cites Rowbotham again, and he claims this is because of the 'very great distances' involved.

I am working through the trig now, but my sense is that quite a large movement in any direction would be required for the markers to line up.

I fixed up a long pole with two red discs on it, the upper one having its centre the same height above the water as the centre of the black band and of the telescope, while the second disc was four feet lower down.

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I didn’t understand why so, at first. But now we have 3 miles length of one side, 4 feet up, this should tell us where the viewer should be in order for the top marker to line up.

[edit] and some v elementary trig suggests that the viewer would have to be at least 2x4 feet = 8 feet higher in order for the top mark to line up with the black horizontal band. Wallace is brilliant.

[edit] and some v elementary trig suggests that the viewer would have to be at least 2x4 feet = 8 feet higher in order for the top mark to line up with the black horizontal band. Wallace is brilliant.

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One of the greatest problems with explaining things to the FE folk is that any side view of such a setup usually have the horizontal dimension compressed by a factor of 1000 or more. They then take that side view and try to interpret things as if that's the way things actually are. The reality is that any side view just looks like a line, as the entire thing is six miles (32,000 feet) long and only 20 feet high. If you were to draw it on piece of paper with the side view 12" wide then all the detail would have to fit in 0.01 inches.

I mention this because it's part of the the problem of how they interpret this experiment, and might lead to spurious objections.

He has just come back, and evaded the 'different angle' objection. He now claims that even if the observation point is shifted up or downwards, right or left, even by a fraction of an inch, the observation will change. He cites Rowbotham again, and he claims this is because of the 'very great distances' involved.

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The thinking seems to be about extremes. The distances are extreme therefore the tolerances for the observer are extreme -ly small. There's no analytical evidence for this.

One could just as well say the tolerances are extremely large, but he chose small because it fits his agenda.

"A weighted base would probably work better. The middle of a canal is flat silt, so it should be fairly straight naturally. Here's a standard patio umbrella base with 1" PVC."

I am really liking this. How about the extendibility aspect? The depth of the water is unknown.

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I don't know. I think there was a reason Wallace used a barge. I think if you try this in real life, you'll find that the setup will be unstable. Silt on the bottom of a canal is unstable stuff - the base will sink, tilt... and this will continue to happen and things will change.

A barge will be more stable. And more stable than a boat with a keel, because the flat bottom resists roll.

I don't know. I think there was a reason Wallace used a barge. I think if you try this in real life, you'll find that the setup will be unstable. Silt on the bottom of a canal is unstable stuff - the base will sink, tilt... and this will continue to happen and things will change.

A barge will be more stable. And more stable than a boat with a keel, because the flat bottom resists roll.

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Barges are tricky though, for the reasons mentioned. I suggest a thorough 'dry' run.

See below for the kitchen table version. Now we have to prove to the [Flat Earth believer] how far the camera was from the bridge, and how far the pole from the bridge, finally how much higher the camera is in the lower picture. [...]

He didn't use a barge for the certified experiment. He used a telescope on one bridge, a flag on the other, and a marker in the middle that was fixed to the ground.

I think this would be preferable to having something in the water, as it's more fixed. Just tricky to demonstrate measurements. I'd hope that the bottom edge of the railway bridge can essentially be used as a marker.

One problem as you can see here, is that from the Welney bridge the canal has a slight curve.

To see the 6 mile bridge you would likely need to move a bit to the right, which might mean you are obscured by that tree

here's a compressed view. Most of the bend is fairly near the bridge. A view from the town side (NW) would work, were it not for the tree. But it looks like you might be okay just going as close to the town side as possible.

Just in case it should prove impractical to use the Old Bedford River itself, I note that there are several other long straight waterways (canals or canalised rivers) in the same general area. For example there is a 6-mile stretch from (roughly) Outwell to Wiggenhall Saint Mary. It is crossed by several road or footpath bridges along that distance, but this is not necessarily a drawback, as the bridges themselves might be useful as observation points or bases for flags, etc. There is an even longer stretch (about 8 miles) a few miles to the NW, passing between Eastree and Turves. It is not absolutely straight, so a direct line of sight above the water would not be possible, but the essential thing is to be able to measure upwards from the surface of a continuous body of water, to serve as an indisputable 'level'.

William Carpenter had a completely different idea. He had a confused idea about straight lines and that straight lines are level lines. In brief he contended:

that the fact that the distant signal appeared below the middle one as far as the middle one did below the cross-hair, proved that the three were in a straight line, and that the earth was flat.

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That's one of those things that's so wrong it's hard to understand. But once you get what he's thinking (or claiming to believe) it's relatively simple. I'd not figured it out before.

He's saying that point 3 is the middle of the telescope, point 2 is the top of the middle target, and point 1 is at the bridge. Since 3->2 is the same as 2->1 he says that means that 3->2->1 is in a straight line, and as they are all the same distance from the water surface that proves that the water surface is flat.

It one of those arguments where the words sound like they are making sense, but contains so many layers of errors that it's hard to know where to begin. But for a start 3 represents a line going out to infinity, not a point at the scope - (and really the 2D level line represents a 3D plane, viewed edge on. 2 and 1 represent 2D projections of 3D points.

Carpenter wrote at length about this idea in his book Water, Not Convex! The Earth Not a Globe, but sadly I can't find an eBook or excerpt.

Here's my attempt at trying to understand. I think I grok, but it's like trying to screw fog.

(This is the best photo I could find, but it should be looking straight along the bottom of the board.) I think he was imagining a view something like this, with the near end of the board as the horizontal reticle, the middle knot as the top of the middle target, and the far end of the board as the calico flag target on the bridge:

A line that's over our head, and level with the level surface of the water on the FE.

Because the theodolite is leveled, the view is level. And because the line has an end, middle and beginning point that are equidistant from each other, the line is level. Therefore it's a straight, level line above a level surface; i.e. the surface of the water on the FE.

Mr Carpenter defines a "straight line" in a manner totally new, as being absolutely identical with a "level line," thus introducing at the outset confusion of terms, and rendering all clear reasoning impossible.

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Mr Carpenter objects to the value of the view in the large telescope, "because it showed but two points, when a comparison had to be instituted between three;" but he omits to state that the telescope itself was placed accurately at the third point, just as was the spirit-level telescope--to the view shown by which he makes no such objection.

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I think, because he wanted to have:
-the telescope leveled with the level water
-a horizontal reticle, which he imagined established a visible beginning point for his imaginary level line.

He objects that the telescope was not leveled, and goes into a long argument, in which the words "straight line" occur four times, and which, whatever meaning is given to that term, is utterly confused and misleading. He says that I [Wallace] intended to prove that the central signal was five feet above a "straight line" joining the two extreme points. This I both intended to prove and did prove, using the word "straight line" in its proper sense; but Mr Carpenter should not impute to me the absurd mistake he makes himself of thinking that there is, or is supposed to be, a rise above the level at the centre point.

In a letter to Hampden, Wallace noted that if one sighted along a line of poles between Old Bedford Bridge and Welney Bridge, the tops should appear to be “rising higher and higher to the middle point, and thence sinking lower and lower to the furthest one.” Carpenter commented as follows:

The surface of the earth is to be seen “rising” and “falling!” How strange! Why, have we not just been provided with the exact amount of curvature in one continuously progressive scale, without any “ups” and “downs,” from eight inches in the first mile, to 130 feet in the fourteenth mile? Is Mr. Wallace right, and all the other scientific men wrong? Does the surface of the earth curvate continuously upwards, or continuously downwards, or, first upwards, then downwards? Is there a gradual incline, a gradual decline, or is there first one then the other? These are questions every thoughtful man will ask.

Nonsense! A thoughtful man would easily understand what Wallace meant.

By reference to the annexed diagram it will be seen why these men [Wallace and Walsh] object to state exactly the point on which they take their stand [the literal point on the Earth on which they claim to stand during the survey]. Suppose them to say, as they probably will, they are always on the top [of the Earth], at A; there they have to show a fall of 10 feet 8 inches in the first four miles either way, 16 feet at the end of five miles, 266 feet at the end of forty miles, 1,944 feet at the end of sixty miles, and so on. But, mark—when they get to the end of the four, five, forty, or sixty miles, they will be required to retrace their steps and make the survey back again, showing, this time, a rise of exactly the same number of feet as before, when they showed a fall. One hundred pounds per mile, Mr. Hampden [the anon. author of the pamphlet, referring to himself in 3rd person] is ready to give to any engineer or surveyor who will take him to any spot in the United Kingdom and show him the rise and fall according to the above table, as laid down in their own standard works. They dare not attempt it!

Mr. Wallace, in the recent survey, said he would take his stand below the top, and show an incline upwards of five feet at the end of the first three miles. Mr. Coulcher and Mr. Walsh say that he has done it; but they both state what is most palpably untrue! At either end of the six miles selected as the field of operation Mr. Wallace would have to prove the continuation of the decline in the proportion above stated. Could he have done this? Is any one so mendacious as to assert that he could? Let the reader bear in mind what is now said, that every statement that has been made with regard to these measurements will be found a tissue of the most daring falsehoods.

The idea of being "always on the top" is something so glaringly absurd that we fail to see its utter impossibility. Squirrels in a revolving cage, felons on a treadmill may be justly compared to these insane philosophers who dare assert and argue that every living man, woman, and child on a revolving globe are one and all "on the top." But the moment you compel these men to show you how they stand on the top, they immediately show a higher curve still! So, then, you find out it is not "the top" after all, but some distance below it, and you are only shown "the top" at a distance of some miles off. All, in fact, that they can do is to make yon look through a glass and say you fancy you see an horizon in the distance. Which horizon you can never reach; for as you approach it, it in turn sinks below "the top," and you see, or fancy you see, another horizon beyond. But the whole subject is so monstrous and fictitious that it. is vain to argue about what can never be proved, except in appearance. And of course snow can be made to look yellow or green by looking through coloured glass. But the snow does not change its colour, nevertheless.

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Carpenter and Hampden were unable to deal with any kind of relativity or ambiguity. They maintained that Wallace was trying to prove that there was a "hill of water," and the central target would be five feet above both the telescope and the bridge.

Wallace again:

Mr Carpenter's "argument" exhibits a total ignorance of the use of the spirit level, and of the simplest principles of optics and geometry. We have three points taken, at equal distances, above what Mr C. maintains to be a true horizontal straight line--the surface of standing water. The eye is placed at one of the extreme points, and, looking at the other two points, they do not coincide, as they must do if in a straight line with the eye. Again, the cross hair in the telescope of the spirit level marks the direction of "the straight line at right angles to the plumb line at the point of observation" (as Mr C. very accurately defines the true level); and as the middle signal appeared considerably below this line, that alone proved that the water surface was not truly level. The distant signal being apparently as much below the middle signal as that was below the cross hair, is absolutely inconsistent with the three being in any straight line, still less with their being in the Carpenterian "straight line," but is perfectly consistent with the three being points in a circle of about the assumed radius of the earth. This is a question of elementary geometry about which there can be no dispute. I may add that the fact of the apparent "equality " of these distances (so dwelt upon by Mr C. in his "argument"), and the views from both extremities of the six miles agreeing so closely, both prove the very great accuracy of the level used, and that it may be depended on to show that the surface of water does really sink below the true level line in a continually increasing degree as the distance is greater; but the proof of convexity in no way depends on this accuracy, as it was shown still better by the large telescope without a spirit level.

The lower curved line represents the supposed curved surface of the water. The points A B C are three points equi-distant above that surface. The top line from A is the level line shown by the cross-hair in the level-telescope. If the water surface had been truly level, the two points B and C must have been cut by the cross-hair. But even if the cross-hair did not show the true level, but pointed upwards, and the water was truly level, then the distant mark, being the same height above the water as the top disc at half the distance and the telescope, these two objects must have appeared in a straight line, the nearer one covering the more distant. It should appear on the straight line drawn from the eye at A through B, whereas it appears a long way below it, thus proving curvature, the essential point to be shown.

Thus the view in the large telescope and in the level-telescope both told exactly the same thing, and, moreover, proved that the curvature was very nearly of the amount calculated from the known dimensions of the earth...

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The top line establishes the astronomical horizon. Both targets are below the astronomical horizon. But no one should think about words such as below, or a rise or fall in the overly literal and rigid way Carpenter and Hampden did.